Pulse shaping network

ABSTRACT

An electrical network for reducing the effective duration of a pulse by increasing the peak amplitude of the pulse within a predetermined portion of its defining bit period relative to the maximum amplitude of such pulse within a predetermined portion of an adjacent bit period, wherein a signal representation of such pulse, an inverter advanced signal representing such pulse, and an inverted retarded signal representing such pulse are combined to generate a combination pulses of reduced effective duration.

United States Patent 1191 Srivastava 1 1 June'S, 1973 54] PULSE SHAPINGNETWORK 3,381,245 4/1968 Guanella ..333 20 [75] Inventor: KeshavaSrivastava, Oklahoma City, gzggzgg i:

Okla- 3,252,093 5/1966 Lerner ..333/20 x [73] Assignee: HoneywellInformation Systems Inc.,

waltham Mass Primary Examiner-Rudolph V. Rolmec Assistant ExaminerMarv1nNussbaum [22] Filed: Dec. 29, 1971 Attorney-Lewis P. Elbinger, Ronald T.Reiling and Fred Jacob [57] ABSTRACT [52] U.S. Cl. ..333/20, 333/28 R,333/31 R,

333/70 T An electncal network for reducing the effectwe dura- 51 Int CL03 7 2 03 7 30 0 3 04 tion Of a pulse by increasing the peak amplitudeof the 581 Field of Search .333/70 T 20 28 Pulse within a Predeterminedof its defining bit 333/18 5 period relative to the maximum amplitude ofsuch pulse within a predetermined portion of an adjacent [56] ReferencesCited bit period, wherein a signal representation of such pulse, aninverter advanced signal representing such UNITED STATES PATENTS pulse,and an inverted retarded signal representing 3 315 171 4/1967 B k 333/28x such pulse are combined to generate a combination ec er 3,292,11012/1966 Becket et al ..333/l8 pulses of reduced effect durat'on' 11Claims, 5 Drawing Figures //4 )I/S DELAY 054w ELEME/VT ELEMENT PuftentedJune 5, 1973 3,737,808

3 Sheets-Sheet 1 Patemed June 5, 173

l/VPUT, :50

X if PULSE SHAPING NETWORK BACKGROUND OF THE INVENTION This inventionrelates to pulse Shaping networks, and more particularly to filters fornarrowing, or reducing the effective duration, of electrical pulses.

In the extraction of the information carried by electrical signaltrains, it is well-known that the maximum amount of accurate informationcan be extracted from such train, or a given amount of information canbe more easily and economically extracted, if the signalto-noise ratioof the train is maximized. Accordingly, in signal train generating andreceiving apparatus attention is directed to equipment maximizing thesignal-tonoise ratio prior to the attempt to extract the informationfrom the train. Such equipment is usually intended to maximize the ratioof the peak amplitude of the information signals relative to theamplitude of the noise signals.

A widely spread technique for communicating information today representsinformation in the form of electrical pulses. A pulse has a definablewidth or time interval of occurrence, and most of the energy of thepulse is concentrated within such time interval. For purposes of theensuing description, the definite interval within which a pulse isintended to occur, and only within which the energy of such pulse willbe considered as representing information will be termed the pulsedefining period.

In one form of pulse-represented information system, theinformation-bearing parts of a signal train comprise a succession ofinformation intervals of uniform duration, each such informationinterval containing a binary digit. The binary digit in an informationinterval is a binary or a binary according to whether or not a pulse ispresent in the information interval. In this information system, abinary digit is termed a bit and an information interval may be termed abit period.

In generating binary digital information for such a system, a bitrepresenting pulse may not be confined within a single bit period, butmay extend over its defining period and one or more adjacent precedingand following bit periods. Bit representing pulses of this type areoften generated in magnetic tape or disc information stores, forexample, in those magnetic stores, the bit pulses are generated by amagnetic sensing transducer which responds to the rate of change ofmagnetic field as the magnetic information bearing medium is moving pastthe transducer.

In extracting information from an information signal train of the typein which each of a succession of uniform duration bit periods containseither a binary 1 represented by a pulse, or a binary 0 represented bythe absence of a pulse, the signal train is sampled during each bitperiod, or during a predetermined portion of each bit period near thecenter thereof, to determine whether or not a pulse is present in thebit period. Whether a pulse is positively, accurately, and easilyrecognized within each bit period in which a binary l is to berepresented and whether the absence ofa pulse is positively, accurately,and easily recognized within each bit period in which a binary 0 is tobe represented depends on the signal-to-noise ratio of the signal train.Thus, the greater the amplitude of the pulses within the pulse definingperiods relative to the amplitude of the noise within the periods inwhich pulses are not intended to be recognized, the easier and moreaccurate is the extraction of the binary digital information from I thesignal train.

It is apparent that any portion of a pulse which extends beyond itsdefining bit period contributes to the noise content in the periodsadjacent to its defining bit period. Such extending pulse portionsreduce the ratio of the peak amplitude of the pulse in its pulsedefining period relative to the peak amplitude of the combinedextraneous pulse and noise signals in adjacent bit periods. Accordingly,to enhance the signal-to-noise ratio of a binary pulse signal train ofthis type, the energy of each pulse should be confined to the extentfeasible to its defining period.

Various techniques have been described in the prior art for recognizingpulses in the presence of noise. Thus, M. Schwartz in InformationTransmission Modulation and Noise, 1959, by McGraw-Hill Book Company,Inc. describes many complexmathematically derived filters of generalapplicability for recognizing pulses in the presence of common noise. Inaddition, many forms of electronic circuits have been disclosed forretiming, reshaping and regenerating pulses in order to provide fortheir conformance with predetermined shape and width specifications.Circuits of this type are described, for example, by R. S. Ledley inDigital Computer and Control Engineering, 1960, McGraw- Hill BookCompany, Inc. However, none of these prior art techniques and circuitshave been directed to the particular problems of providing a pulseshaping network for reducing by a predetermined amount the amplitude ofa pulse outside of its pulse defining bit period, or of narrowing apulse by maximizing the ratio of peak amplitude of the pulse within apredetermined portion of its defining bit period relative to theamplitude of the portion of such pulse extending into a predeterminedportion of an adjacent bit period. Thus, none of these prior arttechniques and circuits have been directed to a precisely designednetwork which maximizes the signal-to-noise ratio of a pulse train inwhich the noise comprises portions of the information pulses.

Accordingly, it is the principal object of this invention to provide animproved network for increasing the signal-to-noise ratio of signaltrains in which information is represented by electrical pulses.

Another object of this invention is to provide a network for narrowing,of reducing the effective duration, or pulses.

Another object of the invention is to provide apparatus for shaping anelectrical pulse within a predetermined one of a succession of intervalsof uniform duration.

Another object of this invention is to provide apparatus for changingthe shape of a pulse existing over a pulse defining bit period and oneor more adjacent preceding and following bit periods.

SUMMARY OF THE INVENTION In accordance with the present inventionapparatus is provided for narrowing a pulse by increasing the from by afirst delay amount, which may be one-half of a bit period. Another delayelement supplies a third signal corresponding to the pulse to be shapedand delayed therefrom by a second delay amount, which may also beone-half of a bit period. A ratio determining means adjusts theamplitudes of the first and third signalsrelative to the amplitude ofthe second signal to represent a first ratio. The first, second andthird signals, with their relative amplitudes so adjusted are applied torespective first, second and third input terminals of a signal combiningmeans, which may be an algebraic adder. The combining means combines thethree signals received thereby according to the predetermined operationwhich it is to perform, such as algebraic addition, and delivers acorresponding output signal, which is the desired narrowed pulse. Theratio determining means is designed to have the first ratio provide amaximum second ratio between the peak amplitude of the output pulsewithin a predetermined portion of its pulse defining bit period and themaximum amplitude of such output pulse within a predetermined portion ofa bit period adjacent to the pulse defining period. Accordingly, anoutput pulse is generated whose energy is more nearly confined to itspulse defining bit period and which contributes minimally to the noisein bit periods adjacent to the pulse defining period.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will be described withreference to the accompanying drawings, wherein:

FIG. 1 illustrates three representative pulses of different widthsrelative to their defining periods;

FIG. 2 is a block diagram of the preferred embodiment of the pulseshaping network of the invention;

FIG. 3 illustrates different output pulses delivered by the network ofFIG. 2 for different values of the network attenuation factor K inresponse to a particular input pulse;

FIG. 4 illustrates for comparison a particular input pulse applied tothe network of FIG. 2 and the corre sponding output pulse delivered bythe network for the optimal value of attenuation factor K; and,

FIG. 5 illustrates a pair of curves representing respectively thevariation of the optimal attenuation factor K and the correspondingsignal-to-noise ratio achieved in the output pulses delivered by thenetwork of FIG. 2 for different values of the width factor 0.

DESCRIPTION OF THE PREFERRED EMBODIMENT The present invention isintended to reduce the effective duration of pulses primarily of thegeneral form shown in FIG. 1. Wen the frequency content of a rectangularelectrical pulse is limited, such as by attenuating or inhibiting thehigher harmonic frequency components of the pulse, the consequentspectral limited pulse takes on the shape of the pulses of FIG. 1,exhibiting rounded corners and acquiring skirts which increase itseffective duration. Pulses of this form are also generated by a magneticsensing transducer which senses the rate of change of magnetic fieldsrepresenting stored binary digits as a magnetic informationbearingmedium is moved past the transducer. The pulses delivered by thetransducer depart from the precise rectangular shape due to the fringingof the magnetic fields defining the stored bits and because of thelimited frequency response to. the transformer itself.

FIG. 1 illustrates how the different pulses shown extend beyond theirrespective defining bit periods into adjacent bit periods, therebycontributing in varying degrees to the noise content in such adjacentbit periods. The type of pulse shown in FIG. 1 is known as a gaussianpulse, which is a pulse whose amplitude versus time configurationconforms to a well-known equation that defines two-dimensionalsymmetrical curves known as gaussian curves. Thus, the symmetricalgaussian pulse has been selected as the vehicle for describing theoperation and defining the design of the network of the presentinvention because it closely approximates the symmetrical pulse whichthe network of the invention is intended to narrow. Moreover, themathematically described gaussian pulse permits a complete and precisemathematical analysis of the design and characteristics of the networkwith which it is employed. However, the present invention is not limitedto narrowing only gaussian type pulses, but may, instead, be employedwith most types of electrical pulses which are required to be narrowed.

Assuming that the pulse to be narrowed by the present invention can becharacterized by its voltage as a function of time, the correspondingsymmetrical gaussian pulse can be represented by the equation:

r-z 2 V=Aewherein:

A is the peak voltage of the pulse,

T is the duration of the bit periods of the signal train in which thepulse occurs,

t represents the time of occurrence of the axis of symmetry of thesymmetrical pulse, and

a is a factor which determines the relative width of the pulse, and,therefore, will be termed hereinafter the width factor. The three pulsesshown in FIG. 1 are gaussian pulses for which the width factors arerespectively 0.30, 0.50 and 0.70. FIG. 1 demonstrates that an increasedwidth factor corresponds to a wider pulse. Thus, the pulse whose widthfactor is 0.30 extends only a small amount beyond its defining bitperiod. On the other hand, the pulses whose width factors are 0.50 and0.70 extend substantially into and across the bit periods adjacent tothe defining bit period.

As explained previously herein, a signal-to-noise ratio for a pulse ofthe type shown in FIG. 1 may be expressed in which the noise comprisesthe portions of the pulse which extend beyond its defining period.Accordingly, if the full duration of the bit periods are considered, thesignal-to-noise ratio of one of these pulses, considering only the noisecontribution of the pulse in the bit period adjacent the defining bitperiod, is the ratio of the maximum voltage, or amplitude, of the pulsewithin the defining bit period to the maximum voltage, or amplitude, ofthe pulse in the adjacent period. This latter value is the voltage ofthe pulse in the immediate vicinity of the boundary between the definingbit period and the adjacent bit period, designated as t in FIG. 1. Forthe pulse whose width factor is 0.30 this signal-to-noise ratio is 4.00,for the pulse whose width factor is 0.50 this signal-to-noise ratio is1.65,

and for the pulse whose width factor is 0.70 this signalto-noise ratiois l.29.

The pulse shaping network shown in FIG. 2, is intended to reduce theeffective duration of pulses which extend beyond the pulse defining bitperiods, thereby improving their signal-to-noise ratio. This network isparticularly adapted to the narrowing of pulses primarily of the generalform shown in FIG. 1. The network provides for the generation of threeseparate signals, each of which corresponds to an input pulse to benarrowed, establishes a predetermined amplitude and polarityrelationship between the three signals, and combines the three signalsaccording to an arithmetic operation to achieve a desired configurationof output pulses which is a narrowed version of the input pulse.

The network shown in FIG. 2 employs one form of transversal filter,described as capable of performing certain types of pulse shaping, shownby R. W. Lucky et al. in Principles of Data Communications, 1968 byMcGraw-Hill Book Company, Inc.

The pulse shaping network of FIG. 2 comprises an input terminal 11 forreceiving the input pulse to be narrowed. A network input lead 12 isconnected to terminal l1 and transmits the input pulse to a first delayelement 14 and a first attenuator inverter 15. Delay element 14 isprovided with an input lead which is connected to input lead 12 forreceiving the input pulse and an output lead which is connected totransmit the delayed output pulse delivered by delay element 14 to asecond delay element 16 and a summing circuit 18. Delay element 16 isprovided with an input lead which is connected to the output lead ofdelay element 14 for receiving the delayed output pulse transmitted bydelay element 14. Delay element 16 is also provided with an output leadwhich is connected to transmit the delayed output pulse delivered bydelay element 14 to a second attenuator inverter 20. Each of delayelements 14 and 16 provides a delay of one-half bit period for pulsestransmitted therethrough.

Attenuator inverters l5 and 20 invert the polarity of the respectivepulses received thereby and reduce, or attenuate, the amplitude of thereceived pulses by respective predetermined amounts. The output signalsdelivered by attenuator inverters and are applied to respective inputleads of summing circuit 18. The amount of attenuation'provided by eachof attenuator inverters l5 and 20 in the embodiment of FIG. 2 is thatwhich provides respective predetermined ratio K and K which are lessthen unity, between the amplitude of respective output pulses deliveredby the attenuator inverter and the amplitude of the respective inputpulse received by the attenuator inverter. The ratios K and K willhereinafter be term ed attenuation factors. Attenuator inverters l5 and20 may take any one of several forms known in the art for producingthe'requisite function. An exemplary form is shown in FIG. 2, whereinattenuator inverter 15 comprises an inverting amplifier 22 connected toa potentiometer 23. The polarity of the input pulse received byattenuator inverter 15 is inverted by inverting amplifier 22 and theconsequent inverter polarity pulse is attenuated by potentiometer 23.The setting of the movable arm of potentiometer 23 determines theattenuation factor K provided by attenuator inverter 15. Similarly,attenuator inverter 20 comprises an inverting amplifier 24 connected toa potentiometer 25. The setting of the movable arm of potentiometer 25determines the attenuation factor K provided by attenuator inverter 20.The inverted and attenuated pulses delivered by attenuator inverters 15and 20 are applied to respective input terminalsof summing circuit 18.

Summing circuit 18 is a device adapted to receive three input signals atthe respective three input terminals thereof and to deliver an outputsignal at the output terminal 27 thereof which represents the algebraicsum of the values represented by the three input signals. The outputsignal delivered at terminal 27 is a pulse which is a narrowed versionof the input pulse received at input terminal 11 of the network.

The values of the attenuation factors K and K are adjusted by therespective potentiometers 23 and 25 to provide a maximum ratio betweenthe peak amplitude of the output pulse delivered at terminal 27 and themaximum amplitude of such output pulse during predetermined portions ofbit periods adjacent to the defining bit period of such pulse. Indetermining the values of attenuation factors K and K the entiredurations of the defining and adjacent bit periods may be employed inanalyzing the amplitudes of the pulse involved, or only predeterminedportions of each of these bit periods may be employed.

The ensuing description will be directed toward an explanation of howthe attenuation factors K and K are determined and their effect on theconsequent output pulse. However, in the disclosed embodimentattenuation factors K and K will be maintained equal and both aredesignated as attenuation factor K hereinafter.

The pulse shaping network of the invention operates, generally, bysubtracting from the input pulse, as represented by the signal appliedto the second input terminal of summing circuit 18 from delay element14, a signal which reduces the skirt of the leading edge of the inputpulse, which is that portion of the pulse occurring prior to itsdefining period, and a signal which reduces the skirt of the trailingedge of the input pulse, which is that portion of the pulse occurringfollowing its defining period. The signal which reduces the skirt of theleading edge of the input pulse is primarily the attenuated invertedrepresentation of the input pulse applied to the first input terminal ofsumming circuit 18 from attenuator inverter 15. The peak of this signalis advanced by one-half bit period relative to the time of occurrence ofthe peak of the pulse applied to the second input terminal of summingcircuit 18. The signal which reduces the skirt of the trailing edge ofthe input pulse is primarily the attenuated inverted representation ofthe input pulse applied to the third input terminal of summing circuit18 from attenuator inverter 20. The peak of this latter signal isretarded by one-half bit period relative to the time of occurrence ofthe peak of the pulse applied to the second input terminal of summingcircuit 18.

These advanced and retarded signal representations of the input pulseare subtracted from the actual signal representation of the input pulseby the algebraic addition operation provided on these three signals bysumming circuit 18. Thus, the leading and trailing skirts of the inputpulse are reduced in accordance with the amplitudes of these advancedand retarded signals. The ratio between the amplitudes of the advancedand retarded pulse representations on one hand and the input pulserepresentation on the other hand is determined by the common attenuationfactor K, controlled by the similar settings of potentiometers 23 and25. a

By way of example FIG. 3 illustrates different-shaped output pulsesdelivered by summing circuit 18 for various values of attenuation factorK when the network receives an input pulse whose width factor is 0.50,which is the pulse for which K 0. FIG. 3 illustrates that the instantinvention reduces the relative amplitudes of the skirts of the inputpulse as the attenuation factor K is increased. Thus, whereas the ratioof the peak amplitude of the input pulse to the amplitude of such pulseat the boundaries of the defining period is approximately 1.65 which isthe aforementioned signalto-noise ratio for the input pulse, this ratiois increased in the output pulse to approximately 2.00 for K 0.20, 2.46for K 0.30, 3.46 for K 0.40 and 3.90 for K 0.42. However, for values ofK greater than 0.42, the maximum amplitude of the output pulse in theadjacent bit period no longer occurs at the boundary t, whereupon usingthis boundary value to represent the signalto-noise ratio becomesmeaningless. Moreover, for values of K greater than 0.42, the ratio ofthe peak amplitude of the output pulse in the defining period to themaximum amplitude of the output pulse in the adjacent periods commencesto decrease.

Accordingly, the attenuation factor K reaches a value, termed itsoptimal value, for which the ratio between the peak amplitude of theoutput pulse in the defining period to the maximum amplitude of theoutput pulse in the adjacent periods is maximum. This optimal value ofK, for a particular input pulse, thereby provides a maximumsignal-to-noise ratio for the corresponding output pulse if the fulldurations of the defining and adjacent bit periods are considered. Foran input pulse whose width factor is 0.50, such optimal value ofattenuation factor K is 0.42. The corresponding maximum signal-to-noiseratio for the output pulse is approximately 3.90. i 1

FIG. 4 affords a comparison of the input and output pulses of a networkof the type shown in FIG. 2, in which the attenuation factor K is settothe optimal value 0.42 for an input pulse whose width facto a is 0.50.The significant reduction in the skirts from the input pulse to theoutput pulse is demonstrated by this figure. This reduction in theskirts of the pulse affords an improvement in signal-to-noise ratio,from 1.65 for the input pulse to approximately 3.90 for the outputpulse, considering the full duration of the defining and adjacent bitperiods.

The optimal value of attenuation factor K for achieving maximumsignal-to-noise ratio for the output pulse varies according to the widthfactor of the input pulse. This variation of the optimal value ofattenuation factor K for input pulses of different width factors isshown by the curve labeled K in FIG. 5. This figure also illustrates, bythe curve designated Z, the maximum signal-to-noise ratio achievable inthe output pulse, considering the full duration of the defining andadjacent bit periods, for the corresponding optimal values ofattenuation factor K.

As has been mentioned previously herein, a signal train may be sampledfor its information content only during predetermined portions of eachbit period, preferably portions which are centered about the center ofeach bit period. The instant invention is also applicable to increasingthe signal-to-noise ratio of pulses utilized in such systems. In suchevent, the pulse portion representing noise in the signal-to-noise ratioof a pulse is not determined by the maximum amplitude of the pulseconsidered across the entire adjacent bit period, but by only themaximum amplitude of the pulse in the sampling portion of the adjacentbit period. It is apparent from FIG. 1 that the signal-to-noise ratio ofan input pulse is greater when the amplitude of such pulse is consideredonly near the center of the adjacent bit period, rather than over theentire adjacent bit period. Therefore, because the amplitude of thepulse at the adjacent bit period boundary does not contribute to thenoise, the optimal values of K will differ for a gaussian pulse ofpredetermined width factor 0. Here, the opti mal value of K is thatwhich maximizes the ratio of the peak amplitude of the output pulse inits defining period to the maximum amplitude of the output pulse in thesampling portion of the adjacent bit period.

In determining the values of attenuation factor K to employ for thenetwork of this invention computer analysis, manual mathematicalanalysis, or graphical combination of curves representing pulses may beemployed. All of these techniques are well known in the art; Althoughparticular values of the delay provided by delay elements 14 and 16 havebeen specified in the illustrated embodiment, it is within the scope ofthis invention to provide other and different values for both suchelements where an input pulse is not representable by the gaussian form,or is unsymmetrical, the abovedescribed analytical technique may beemployed to determine these values for optimum signal-to-noise ratioimprovement.

Thus, there has been described herein a novel and improved network forreducing the effective duration of electrical pulses by confining theenergy of such pulses more nearly to their pulse defining period. Thepulses delivered by the network of the invention exhibit a substantiallyincreased signal-to-noise ratio over the received pulses.

While the principles of the invention have now been made clear inillustrative embodiment, there will be immediately obvious to thoseskilled in the art many modifications in structure, arrangements,proportions, the elements, materials, and components used in thepractice of the invention, and otherwise, which are particularly adaptedfor specific environments and operating requirements, without departingfrom these principles. The appended claims are therefore intended tocover and embrace any such modification, within the limits only of thetrue spirit and scope of the invention.

What is claimed is:

1. Apparatus for shaping an electrical pulse within one of a successionof intervals of uniform duration and which extends beyond said oneinterval so as to contribute to the noise content in an adjacentinterval, comprising means responsive to said pulse for supplying afirst signal corresponding to said pulse;

means responsive to said pulse for supplying a second signalcorresponding to said pulse and delayed therefrom by a first delayamount;

means responsive to said pulse for supplying a third signalcorresponding to said pulse and delayed therefrom by a second delayamount;

ratio determining means responsive to at least one of said first, secondand third signals for providing that the amplitudes of said first andthird signals relative to the amplitude of said second signal representa first ratio;

combining means having first, second and third input terminals forreceiving respective input signals and an output terminal, saidcombining means performing a predetermined combinatorial operation onthe signals received at said input terminals and delivering an outputsignal at said output terminal representing the result of saidcombinatorial operation; and

means for coupling said first, second and third signals respectively tosaid first, second and third input terminals;

said ratio determining means designed to have said first ratio provide amaximum second ratio between the maximum amplitude of said output signalwithin a predetermined portion of said one interval and the maximumamplitude of said output signal during a predetermined portion ofanother of said intervals adjacent to said one interval so as to confinesaid output signal to said one interval.

2. The apparatus of claim 1, wherein said first delay amount is equal toone-half the duration of one of said intervals and said second delayamount is equal to the full duration of one of said intervals.

3. The apparatus of claim 2, wherein said combinatorial operationperformed by said combining means on said first, second and thirdsignals is an algebraic addition operation.

4. The apparatus of claim 3, wherein said first and third signals are ofopposite polarity to said second signal.

5. The apparatus of claim 4, wherein said predetermined portion of saidone interval comprises the entirety of said one interval and saidpredetermined portion of said adjacent interval comprises the entiretyof said adjacent interval.

6. The apparatus of claim 4, wherein said first ratio is determined fora gaussian pulse closely approximating said electrical pulse and saidmaximum second ratio is determined for said output signal as deliveredin re-' sponse to first, second and third signals which correspond tosaid gaussian pulse.

7. A pulse shaping network for changing the shape of an electrical pulseoccurring over at least consecutive first and second intervals, one ofsaid intervals corresponding to a defining interval for said pulse,comprising:

a network input lead for receiving said pulse;

first and second delay elements, each of said delay elements havingrespective input and output leads, the input lead of said first delayelement being connected to said network input lead and the output leadof said first delay element being connected to the input lead of saidsecond delay element;

a first attenuator inverter, said first inverter having an input leadfor receiving an input signal and an output lead for delivering anoutput signal, the amplitude of the output signal delivered by saidfirst inverter representing a first ratio relative to the amplitude ofthe input signal received thereby, said ratio being less than unity, andthe polarity of the output signal delivered by said first inverter beingopposite to the polarity of the input signal received thereby, the inputlead of said first inverter being coupled to the input lead of saidfirst delay element;

second attenuator inverter, said second inverter having an input leadfor receiving an input signal and an output lead for delivering anoutput signal, the amplitude of the signal delivered by said secondinverter representing a second ratio relative to the amplitude of theinput signal received thereby, said second ratio being less than unity,and the polarity of the output signal delivered by such second inverterbeing opposite to the polarity of the input signal received thereby, theinput lead of said second inverter being coupled to the output lead ofsaid second delay element;

a summing means having first, second and third input terminals forreceiving respective input signals and an output terminal, said summingmeans performing an algebraic addition operation on the signals receivedat said input terminals and delivering an output signal at said outputterminal representing the algebraic sum of the values represented by thethree input signals received at said input terminals; and

means for coupling the first input terminal of said summing means to theoutput lead of said first inverter, for coupling the second inputterminal of said summing means to the output lead of said first delayelement, and for coupling the third input terminal of said summing meansto the output lead of said second inverter;

said first and second ratios being selected to provide a maximum thirdratio between the maximum amplitude of said summing means output signalwithin a predetermined portion of said second interval and the maximumamplitude of said summing means output signal during a predeterminedportion of said first interval whereby said output signal is confined tosaid defining interval.

8. The network of claim 7, wherein the amount of delay provided by eachof said first and second delay elements is equal to one-half theduration of said second interval.

9. The network of claim 8, wherein said predetermined portion of saidfirst interval comprises the entirety of said first interval and saidpredetermined portion of said second interval comprises the entirety ofsaid second interval.

10. The network of claim 9, wherein said first and second ratios areequal and are determined for a gaussian pulse closely approximating saidelectrical pulse and said maximum third ratio is determined for saidoutput signal of said summing means as delivered in response to theapplication of said gaussian pulse to said network input lead.

11. The network of claim 8, wherein said first and second ratios aredetermined for a gaussian pulse closely approximating said electricalpulse and said maximum third ratio is determined for said output signalas delivered by said summing means in response to the application ofsaid gaussian pulse to said network input lead.

1. Apparatus for shaping an electrical pulse within one of a successionof intervals of uniform duration and which extends beyond said oneinterval so as to contribute to the noise content in an adjacentinterval, comprising means responsive to said pulse for supplying afirst signal corresponding to said pulse; means responsive to said pulsefor supplying a second signal corresponding to said pulse and delayedtherefrom by a first delay amount; means responsive to said pulse forsupplying a third signal corresponding to said pulse and delayedtherefrom by a second delay amount; ratio determining means responsiveto at least one of said first, second and third signals for providingthat the amplitudes of said first and third signals relative to theamplitude of said second signal represent a first ratio; combining meanshaving first, second and third input terminals for receiving respectiveinput signals and an output terminal, said combining means performing apredetermined combinatorial operation on the signals received at saidinput terminals and delivering an output signal at said output terminalrepresenting the result of said combinatorial operation; and means forcoupling said first, second and third signals respectively to saidfirst, second and third input terminals; said ratio determining meansdesigned to have said first ratio provide a maximum second ratio betweenthe maximum amplitude of said output signal within a predeterminedportion of said one interval and the maximum amplitude of said outputsignal during a predetermined portion of another of said intervalsadjacent to said one interval so as to confine said output signal tosaid one interval.
 2. The apparatus of claim 1, wherein said first delayamount is equal to one-half the duration of one of said intervals andsaid second delay amount is equal to the full duration of one of saidintervals.
 3. The apparatus of claim 2, wherein said combinatorialoperation performed by said combining means on said first, second andthird signals is an algebraic addition operation.
 4. The apparatus ofclaim 3, wherein said first and third signals are of opposite polarityto said second signal.
 5. The apparatus of claim 4, wherein saidpredetermined portion of said one interval comprises the entirety ofsaid one interval and said predetermined portion of said adjacentinterval comprises the entirety of said adjacent interval.
 6. Theapparatus of claim 4, wherein said first ratio is determined for agaussian pulse closely approximating said electrical pulse and saidmaximum second ratio is determined for said output signal as deliveredin response to first, second and third signals which correspond to saidgaussian pulse.
 7. A pulse shaping network for changing the shape of anelectrical pulse occurring over at least consecutive first and secondintervals, one of said intervals corresponding to a defining intervalfor said pulse, comprising: a network input lead for receiving saidpulse; first and second delay elements, each of said delay elementshaving respective input and output leads, the input lead of said firstdelay element being connected to said network input lead and the outputlead of said first delay element being connected to the input lead ofsaid second delay element; a first attenuator inverter, said firstinverter having an input lead for receiving an input signal and anoutput lead for delivering an output signal, the amplitude of the outputsignal delivered by said first inverter representing a first ratiorelative to the amplitude of the input signal received thereby, saidratio being less than unity, and the polarity of the output signaldelivered by said first inverter being opposite to the polarity of theinput signal received thereby, the input lead of said first inverterbeing coupled to the input lead of said first delay element; a secondattenuator inverteR, said second inverter having an input lead forreceiving an input signal and an output lead for delivering an outputsignal, the amplitude of the signal delivered by said second inverterrepresenting a second ratio relative to the amplitude of the inputsignal received thereby, said second ratio being less than unity, andthe polarity of the output signal delivered by such second inverterbeing opposite to the polarity of the input signal received thereby, theinput lead of said second inverter being coupled to the output lead ofsaid second delay element; a summing means having first, second andthird input terminals for receiving respective input signals and anoutput terminal, said summing means performing an algebraic additionoperation on the signals received at said input terminals and deliveringan output signal at said output terminal representing the algebraic sumof the values represented by the three input signals received at saidinput terminals; and means for coupling the first input terminal of saidsumming means to the output lead of said first inverter, for couplingthe second input terminal of said summing means to the output lead ofsaid first delay element, and for coupling the third input terminal ofsaid summing means to the output lead of said second inverter; saidfirst and second ratios being selected to provide a maximum third ratiobetween the maximum amplitude of said summing means output signal withina predetermined portion of said second interval and the maximumamplitude of said summing means output signal during a predeterminedportion of said first interval whereby said output signal is confined tosaid defining interval.
 8. The network of claim 7, wherein the amount ofdelay provided by each of said first and second delay elements is equalto one-half the duration of said second interval.
 9. The network ofclaim 8, wherein said predetermined portion of said first intervalcomprises the entirety of said first interval and said predeterminedportion of said second interval comprises the entirety of said secondinterval.
 10. The network of claim 9, wherein said first and secondratios are equal and are determined for a gaussian pulse closelyapproximating said electrical pulse and said maximum third ratio isdetermined for said output signal of said summing means as delivered inresponse to the application of said gaussian pulse to said network inputlead.
 11. The network of claim 8, wherein said first and second ratiosare determined for a gaussian pulse closely approximating saidelectrical pulse and said maximum third ratio is determined for saidoutput signal as delivered by said summing means in response to theapplication of said gaussian pulse to said network input lead.